Regularity of inviscid shell models of turbulence

Peter Constantin, Boris Levant, Edriss S. Titi

Research output: Contribution to journalArticle

25 Scopus citations

Abstract

In this paper we continue the analytical study of the sabra shell model of energy turbulent cascade. We prove the global existence of weak solutions of the inviscid sabra shell model, and show that these solutions are unique for some short interval of time. In addition, we prove that the solutions conserve energy, provided that the components of the solution satisfy |un|≤C kn -1/3 [n log(n+1)] -1 for some positive absolute constant C, which is the analog of the Onsager's conjecture for the Euler's equations. Moreover, we give a Beal-Kato-Majda type criterion for the blow-up of solutions of the inviscid sabra shell model and show the global regularity of the solutions in the "two-dimensional" parameters regime.

Original languageEnglish (US)
Article number016304
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume75
Issue number1
DOIs
StatePublished - Jan 26 2007

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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